Wednesday, October 28, 2015

It’s All in the Numbers - Sizes in Nature


If all the animal species are broken up into groups, the light 
blue section includes insects, and the rest of the 
circle colors represent every other animal on Earth!
Comparisons help to make very big or very small numbers meaningful, and biology is chock full of big and small numbers. For instance, there are more insects in the world than there are humans. By more, I mean ALOT MORE, something like 1.5 x 1018 insects. But what does that number mean? Consider looking at it this way; the world population hit 7 billion last year and that's a big number, but even if we were to double our population again in the next ten minutes, there would still be 100 million insects for every human on earth. This certainly makes an impression, but it seems small when comparing the most numerous organisms, bacteria, to humans.

Bacteria outnumber us by orders of magnitude more than insects do; they live everywhere, in every environment. They have been found in 0.5 million year-old permafrost as well as 40 miles up in the atmosphere. There are approximately 100 million to 1 billion bacteria in every teaspoon of dirt, so in total there are currently 5 x1030 bacteria carrying out their daily routines. That means there are about 5 x 1019 living bacteria (that is 50,000,000,000,000,000,000) for every person who has EVER LIVED. Another way of visualizing this might be to imagine that each bacterium is a penny being stacked. The column would be a trillion light years high. That’s about five times the diameter of the observable universe.


Nanobacteria are still controversial, the 0.2 µm diameter is 
close to the smallest size that could still hold DNA. 
For comparison, the white line in panel A is 1 µm long, 
and in Panel C the line is just 0.1 µm.
While the redwoods might be slightly taller than the sequoias, 
the mass of the sequoias is much greater because the 
trunks have such a large diameter.
Even using comparisons and analogies, these numbers are almost too big to comprehend. It isn’t much easier when talking about sizes. The scale of life is amazing, from the smallest bacteria (called nanobacteria), just 0.2 µm in size (1/5,000,000 of a meter), to the biggest living thing on Earth, a Giant Sequoia called General Sherman. This behemoth of a tree is more than 83 meters (272 ft.) in height and 1,225,000 kilograms (2,701,000 lb.) in mass. This means that from smallest to largest, life spans more than eight orders of magnitude. In terms of biomass, the difference between the smallest bacterium and General Sherman is even greater, about 1 x 1023, about the same as difference in mass as one human compared to seven Earths.

On a smaller scale, the difference in size between bacteria and nucleated cells (eukaryotic cells) is still pretty stunning. A single macrophage cell of your immune system can ingest more than 100 bacteria without flinching, and macrophages are nowhere near the biggest eukaryotic cells. These different sizes demand some distinctions in how cells conduct their business; for example, how they move molecules into and within themselves.


A macrophage reaching out and ingesting bacteria.
The bacteria are the small, connected rods.
Eukaryotic cells, unlike prokaryotic cells (bacteria and Archaea), have specialized systems, like actin filaments, cytoskeleton, and microtubules. These apparatus are designed to act like conveyor belts; they carry different molecules through the cell to their needed destinations. Eukaryotes also have specific receptors for bringing in specific molecules. These are fast systems of uptake and movement, and can work against a concentration gradient.


The cytoskeleton of the eukaryotic cell stretch out like fibers.
They help it move, can convey molecules from place to place,
and holds the cells shape.




Unfortunately, bacteria only have diffusion to move molecules around their insides. This makes things doubly hard on them because bacteria have limited access to resources; most often they meet up with few molecules that are important to them (being a small cell in a big environment). Therefore, they need to get as many of these resources into their cell as possible and move throughout their entire volume quickly.

Diffusion is the movement of molecules from places where there a lot of them toward places here there are fewer of them (from high concentration to low concentration). Think of a crowd pouring out onto the football field after a big win. You start with many people in the stands and very few on the field, but end up with about an equal number of people in all parts of the stadium. Bacteria count on consuming their nutrients this way. Important molecules diffuse into the cell, and then get metabolized for energy or other building blocks. This breaking down and reassembly of molecules helps ensure that the concentration of important molecules is always lower inside the cell, so diffusion into the cell can continue. Importantly, as the width or length of a cell doubles, the volume increases by a factor of eight; therefore, prokaryotic cells remain small so that they can get molecules everywhere they need them quickly. It is the only way for diffusion to remain profitable for them.


Diffusion is the movement of from where there are 
many to where there are few. If it is water 
molecules that are moving, then call it osmosis.
Diffusion is not quite as simple as people pouring out the stands. There are several aspects of this process that are important to bacteria. The first of these is the diffusion rate, which is based on a diffusion coefficient for each different molecule, and the liquid it is moving through. For oxygen moving through water, the diffusion rate is about 1 mm/hr. This means that for an average sized bacteria it only takes 1 millisecond (1/1000th of a second) for an oxygen molecule to travel across the entire cell.

There is also the mixing rate; this refers to the time it takes for a molecule that enters the cell to have an equal probability of being found in any part of the cell. A 1µm (1/1,000,000 of a meter) bacterium has a mixing time of roughly 1 millisecond. But since the volume increases by a factor of eight as the size doubles, it would not take much growth for the mixing time to become problematic if a cell was to rely on diffusion alone.

Finally, there is the issue of traffic time. Every reaction that takes place in a cell involves two or more molecules finding one another and then interacting. In both prokaryotic and eukaryotic cells there are some systems designed to help bring molecules together, but in the end, it is basically luck – they have to run into one another. The number of molecules can affect this time; say you want molecule A to meet molecule B. If the cell contained only one of each molecule, this could take a while, but if there are 1000A’s and 1000B’s, then the traffic time will be decreased considerably. For average sized bacteria, traffic times exist in the range of 1 second, but again, if they are much bigger, the chances of molecules meeting their partners goes down dramatically.

If the bacterium grows too big, the diffusion rate, mixing time, and traffic time can become too long to permit survival. Therefore, size limitations seem to be set for bacteria. However, some bacteria just have to be rule breakers. There are two excellent examples of bacteria that have evolved ways to overcome the diffusion problems associated with increased size, and we'll start to look at them next week.



Schulz, H., & Jørgensen, B. (2001). Big Bacteria Annual Review of Microbiology, 55 (1), 105-137 DOI: 10.1146/annurev.micro.55.1.105



For more information on numbers in nature, diffusion, and cytoskeleton, as well as web-based activities and experiments, go to:

Cell size and volume:
http://staff.jccc.net/pdecell/cells/cellsize.html
faculty.massasoit.mass.edu/whanna/121_assets/15-week_2_prelab.pdf
http://www.youtube.com/watch?v=qdvKM1m0jnE
http://www.cellsalive.com/howbig.htm
www.nsa.gov/academia/_files/collected_learning/high.../surface_area.pdf
www.smccd.net/accounts/bucher/modules/DuzSizeMatter.pdf
http://www.accessexcellence.org/AE/AEC/AEF/1996/deaver_cell.php


scaling in nature:
http://www.nature.com/scitable/content/the-sizes-of-organisms-span-21-orders-15321100
http://learn.genetics.utah.edu/content/begin/cells/scale/
http://www.dnatube.com/video/596/Size-Analogies-of-Bacteria-and-Viruses
http://www.smithsonianeducation.org/educators/lesson_plans/size_shapes_animals/index.html


diffusion:
http://www.biologycorner.com/bio1/diffusion.html
http://highered.mcgraw-hill.com/sites/0072495855/student_view0/chapter2/animation__how_diffusion_works.html
http://staff.jccc.net/pdecell/cells/diffusion.html
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/diffus.html
http://www.wisc-online.com/objects/ViewObject.aspx?ID=ap1903
http://www.biologycorner.com/2009/09/16/diffusion-lab/
http://chem.lapeer.org/Bio1Docs/Diffusion.html
http://www.biologyjunction.com/osmosis__diffusion_in_egg_lab.htm
http://phet.colorado.edu/en/contributions/view/3415


cytoskeleton:
http://www.cellsalive.com/cells/cytoskel.htm
http://www.youtube.com/watch?v=5rqbmLiSkpk
http://www.biochemweb.org/cytoskeleton.shtml
http://www.biology.arizona.edu/cell_bio/tutorials/cytoskeleton/page1.html
http://www.biology.arizona.edu/cell_bio/tutorials/cytoskeleton/main.html
http://www.youtube.com/watch?v=zlYyoi5vpE8